{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2000:WWQ3OIWHWT5MBTGAECD7WUHBJP","short_pith_number":"pith:WWQ3OIWH","canonical_record":{"source":{"id":"gr-qc/0005050","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-05-15T22:45:13Z","cross_cats_sorted":[],"title_canon_sha256":"a0c99a6cdbf912870b480148661248f66ab9e2834cf004ba76c433dcda3dc017","abstract_canon_sha256":"0f4acf68b7a70db0d86b01e53c98a29f0586ffa4ddbfeff21f52c14009748ad6"},"schema_version":"1.0"},"canonical_sha256":"b5a1b722c7b4fac0ccc02087fb50e14bdb7d98fc4ec17d03615dac1dfb3c8bb4","source":{"kind":"arxiv","id":"gr-qc/0005050","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0005050","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0005050v2","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0005050","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"WWQ3OIWHWT5M","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"WWQ3OIWHWT5MBTGA","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"WWQ3OIWH","created_at":"2026-07-04T17:22:12Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2000:WWQ3OIWHWT5MBTGAECD7WUHBJP","target":"record","payload":{"canonical_record":{"source":{"id":"gr-qc/0005050","kind":"arxiv","version":2},"metadata":{"license":"","primary_cat":"gr-qc","submitted_at":"2000-05-15T22:45:13Z","cross_cats_sorted":[],"title_canon_sha256":"a0c99a6cdbf912870b480148661248f66ab9e2834cf004ba76c433dcda3dc017","abstract_canon_sha256":"0f4acf68b7a70db0d86b01e53c98a29f0586ffa4ddbfeff21f52c14009748ad6"},"schema_version":"1.0"},"canonical_sha256":"b5a1b722c7b4fac0ccc02087fb50e14bdb7d98fc4ec17d03615dac1dfb3c8bb4","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T17:22:12.471707Z","signature_b64":"kJKWq/nhi6cGlMuouzrAzUiYuwJsl2tQC0B7JKgPwg/5JC7BkN4DGZh4UHA+/HtFWdGqT3uYzmohaPqbZQvLBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b5a1b722c7b4fac0ccc02087fb50e14bdb7d98fc4ec17d03615dac1dfb3c8bb4","last_reissued_at":"2026-07-04T17:22:12.471293Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T17:22:12.471293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"gr-qc/0005050","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T17:22:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9vIT7kWpef6x5QV5q1q817Ttm4qorlhPR3dwFSV35Swa/nnVHwodGfPh8Ym8+AGs7WaPqNEdFlEe6nzDjCMaBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T21:33:17.089759Z"},"content_sha256":"6513da59e4415e72cc80f69c85e19dc9972c2b61b5c53a8f36a68fc855d036c7","schema_version":"1.0","event_id":"sha256:6513da59e4415e72cc80f69c85e19dc9972c2b61b5c53a8f36a68fc855d036c7"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2000:WWQ3OIWHWT5MBTGAECD7WUHBJP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The geometry of photon surfaces","license":"","headline":"","cross_cats":[],"primary_cat":"gr-qc","authors_text":"Clarissa-Marie Claudel, G.F.R. Ellis, K.S. Virbhadra","submitted_at":"2000-05-15T22:45:13Z","abstract_excerpt":"The photon sphere concept in Schwarzschild space-time is generalized to a definition of a photon surface in an arbitrary space-time. A photon sphere is then defined as an SO(3)xR-invariant photon surface in a static spherically symmetric space-time. It is proved, subject to an energy condition, that a black hole in any such space-time must be surrounded by a photon sphere. Conversely, subject to an energy condition, any photon sphere must surround a black hole, a naked singularity or more than a certain amount of matter. A second order evolution equation is obtained for the area of an SO(3)-in"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0005050","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/gr-qc/0005050/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-04T17:22:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDTGeFFnDJgsJxr5sfLc05Wm3e2ZCnwiULlyzGi0FwOgm/7BY9LOjkvsbHqLuhBBa5HeOoaF+JV+LR4grk3+Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T21:33:17.091252Z"},"content_sha256":"556576125e4a53155f14a2d3749398713d0a545ba1e34ee16cd5f8315b12aee7","schema_version":"1.0","event_id":"sha256:556576125e4a53155f14a2d3749398713d0a545ba1e34ee16cd5f8315b12aee7"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWQ3OIWHWT5MBTGAECD7WUHBJP/bundle.json","state_url":"https://pith.science/pith/WWQ3OIWHWT5MBTGAECD7WUHBJP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWQ3OIWHWT5MBTGAECD7WUHBJP/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-09T21:33:17Z","links":{"resolver":"https://pith.science/pith/WWQ3OIWHWT5MBTGAECD7WUHBJP","bundle":"https://pith.science/pith/WWQ3OIWHWT5MBTGAECD7WUHBJP/bundle.json","state":"https://pith.science/pith/WWQ3OIWHWT5MBTGAECD7WUHBJP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWQ3OIWHWT5MBTGAECD7WUHBJP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2000:WWQ3OIWHWT5MBTGAECD7WUHBJP","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"0f4acf68b7a70db0d86b01e53c98a29f0586ffa4ddbfeff21f52c14009748ad6","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2000-05-15T22:45:13Z","title_canon_sha256":"a0c99a6cdbf912870b480148661248f66ab9e2834cf004ba76c433dcda3dc017"},"schema_version":"1.0","source":{"id":"gr-qc/0005050","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"gr-qc/0005050","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"arxiv_version","alias_value":"gr-qc/0005050v2","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.gr-qc/0005050","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"pith_short_12","alias_value":"WWQ3OIWHWT5M","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"pith_short_16","alias_value":"WWQ3OIWHWT5MBTGA","created_at":"2026-07-04T17:22:12Z"},{"alias_kind":"pith_short_8","alias_value":"WWQ3OIWH","created_at":"2026-07-04T17:22:12Z"}],"graph_snapshots":[{"event_id":"sha256:556576125e4a53155f14a2d3749398713d0a545ba1e34ee16cd5f8315b12aee7","target":"graph","created_at":"2026-07-04T17:22:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/gr-qc/0005050/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"The photon sphere concept in Schwarzschild space-time is generalized to a definition of a photon surface in an arbitrary space-time. A photon sphere is then defined as an SO(3)xR-invariant photon surface in a static spherically symmetric space-time. It is proved, subject to an energy condition, that a black hole in any such space-time must be surrounded by a photon sphere. Conversely, subject to an energy condition, any photon sphere must surround a black hole, a naked singularity or more than a certain amount of matter. A second order evolution equation is obtained for the area of an SO(3)-in","authors_text":"Clarissa-Marie Claudel, G.F.R. Ellis, K.S. Virbhadra","cross_cats":[],"headline":"","license":"","primary_cat":"gr-qc","submitted_at":"2000-05-15T22:45:13Z","title":"The geometry of photon surfaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"gr-qc/0005050","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:6513da59e4415e72cc80f69c85e19dc9972c2b61b5c53a8f36a68fc855d036c7","target":"record","created_at":"2026-07-04T17:22:12Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"0f4acf68b7a70db0d86b01e53c98a29f0586ffa4ddbfeff21f52c14009748ad6","cross_cats_sorted":[],"license":"","primary_cat":"gr-qc","submitted_at":"2000-05-15T22:45:13Z","title_canon_sha256":"a0c99a6cdbf912870b480148661248f66ab9e2834cf004ba76c433dcda3dc017"},"schema_version":"1.0","source":{"id":"gr-qc/0005050","kind":"arxiv","version":2}},"canonical_sha256":"b5a1b722c7b4fac0ccc02087fb50e14bdb7d98fc4ec17d03615dac1dfb3c8bb4","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b5a1b722c7b4fac0ccc02087fb50e14bdb7d98fc4ec17d03615dac1dfb3c8bb4","first_computed_at":"2026-07-04T17:22:12.471293Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T17:22:12.471293Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"kJKWq/nhi6cGlMuouzrAzUiYuwJsl2tQC0B7JKgPwg/5JC7BkN4DGZh4UHA+/HtFWdGqT3uYzmohaPqbZQvLBQ==","signature_status":"signed_v1","signed_at":"2026-07-04T17:22:12.471707Z","signed_message":"canonical_sha256_bytes"},"source_id":"gr-qc/0005050","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6513da59e4415e72cc80f69c85e19dc9972c2b61b5c53a8f36a68fc855d036c7","sha256:556576125e4a53155f14a2d3749398713d0a545ba1e34ee16cd5f8315b12aee7"],"state_sha256":"e50a920d160a9386118b2d5ef88568e1c3261a69b251b8ed9db54c11dc54cbb4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Tzwh59hYmi3Bw/AOf6H0qFbElAvwpwhctv26D0KBRddp71JB/ycMbU1KHoabk8XPPa+JWEtoiPp6kwBEpgFnBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T21:33:17.097538Z","bundle_sha256":"c1d9b0ce2612d8a49b284bafc801ddd2ca93169eb9d73bab087326503de50a12"}}